Growth behavior and electronic properties of Ge_(n+1) and AsGe_n(n = 1–20) clusters: a DFT study

We present a systematic computational study based on the density functional theory(DFT) aiming to high light the possible effects of one As doping atom on the structural, energetic, and electronic properties of different isomers of Ge_(n+1) clusters with n = 1–20 atoms. By considering a large number of structures for each cluster size, the lowest-energy isomers are determined. The lowest-energy isomers reveal three-dimensional structures starting from n = 5. Their relative stability versus atomic size is examined based on the calculated binding energy, fragmentation energy, and second-order difference of energy. Doping Ge_(n+1) clusters with one As atom does not improve their stability. The electronic properties as a function of the atomic size are also discussed from the calculated HOMO–LUMO energy gap, vertical ionization potential, vertical electron affinity, and chemical hardness. The obtained results are significantly affected by the inclusion of one As atom into a Gen cluster.

The integral equations of Compton Scatter Tomography

Two new Compton Scatter Tomography modalities, which are aimed at imaging hidden structures in bulk matter for industrial non-destructive control (or testing) and for medical diagnostics are shown to be based on the solutions of a special class of Chebyshev integral transforms. Besides their remarkable analytic properties, they can be inverted by existing methods which lend themselves nicely to numerical treatment and provide convergent, stable and fast computation algorithms. The existence of explicit inversion formulas implies that viable new imaging techniques can be developed, which may take over the current ones in a near future.

Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

我们考虑在磁盘上并且在上面的一半上描述 tricritical Ising 模型的最小的保角的模型飞机。用库仑气体形式主义，我们象它的一个点和二点的关联功能一样决定它的 consistents 边界状态。

DKP Oscillator in a Noncommutative Space

我们在场旋转的 DKP 振荡器模型 0 和 1，在一个 noncommutative 空格。在纺纱 0 的情况中，方程被归结为 KleinGordon 振荡器类型，波浪功能然后被推出，与 DKP 相比，无纺纱的粒子使遭到了到一个经常的磁场的相互作用。为纺纱 1 的盒子，这个问题与在描述与取决于 noncommutativity 参数的另外的修正受到一个经常的磁场的行动的一个 vectorial 波色子的运动的一个可交换的空格的纺纱 1 的 DKP 方程的行为是相等的。

Capillary effect on the sloshing of a fluid in a rectangular tank submitted to sinusoidal vertical dynamical excitation

Surface tension effects on fluid sloshing in a tank subjected to external excitation has been less studied. This work aims at understanding this phenomenon in order to derive practical solutions to problems faced in several engineering. A tank containing a fluid with a free surface is submitted to gravity and capillary forces and subject to external dynamic excitation. Introduction of vertical sinusoidal dynamical excitation leads to a problem of paramtric oscillations governed by the Mathieu equation. Analysis of the Mathieu equation shows the existence of stable and unstable regions in the stability diagram. Some results induced by harmonic excitations on the fluid sloshing are presented. When the external dynamical excitation amplitude ~ is small, periodic solutions appear in stable regions and when e increases, the fluid behavior is not perfectly periodic and the amplitudes are not regular. Nonlinear effects make the behavior of the fluid complicated and render it almost unpredictable. In stable regions, the solution remains bounded at any time. When changing the perturbation parameter 6, the phase difference increases and also with the increase of the surface tension.

Positivity in electron-positron scattering:testing the axiomatic quantum field theory principles and probing the existence of UV states

We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders.First,if positivity is violated,probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the S-matrix theory.We observe that positivity violation at scales of 1-10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present.Second,the positive nature of the dimension-8 parameter space often allows us to either directly infer the existence of UV-scale particles together with their quantum numbers or exclude them up to certain scales in a model-independent way.In particular,dimension-8 positivity plays an important role in the test of the Standard Model.If no deviations from the Standard Model are observed,it allows for simultaneous exclusion limits on all kinds of potential UV-complete models.Unlike the dimension-6 case,these limits apply regardless of the UV model setup and cannot be removed by possible cancellations among various UV contributions.This thus consists of a novel and universal test to confirm the Standard Model.We demonstrate with realistic examples how all the previously mentioned possibilities,including the test of positivity violation,can be achieved.Hence,we provide an important motivation for studying dimension-8 operators more comprehensively.

无能隙量子自旋液体和正方晶格自旋1/2阻挫反铁磁模型的相图

自高温超导发现以来,正方晶格上由自旋为1/2构成的包括近邻和次近邻海森堡相互作用的阻挫反铁磁模型,即J1±J2模型,因其基态被认为可以作为铜基超导的母态,在过去30多年中得到了广泛关注和深入研究.该模型包含的相互作用形式简单,如今也成为用来研究正方晶格上阻挫磁性的基本理论模型.但其基态性质仍然是一个悬而未决的问题.本文作者利用最近发展的二维张量网络态算法,对该模型进行了迄今为止精度最高的计算.详细的数值结果表明这个体系的基态包含了一个无能隙的量子自旋液体和价键固体态.他们进一步计算了相变的临界指数,提出了一个低能有效理论来描述这个量子自旋液体,并探讨了这个量子自旋液体与解禁闭量子临界性的关系.该工作通过仔细比较二维张量网络态和人们常用的密度矩阵重整化群两种算法的结果,提供了在正方晶格阻挫磁性体系的研究上第一个超越密度矩阵重整化方法的例子.他们也解释了以前研究结果矛盾之处的来源,为用二维张量网络态解决量子多体问题提供了一个范本.

CDS:A Fold-change Based Statistical Test for Concomitant Identification of Distinctness and Similarity in Gene Expression Analysis

The problem of identifying differential activity such as in gene expression is a major defeat in biostatistics and bioinformatics. Equally important, however much less frequently studied, is the question of similar activity from one biological condition to another. The fold- change, or ratio, is usually considered a relevant criterion for stating difference and similarity between measurements. Importantly, no statistical method for concomitant evaluation of similarity and distinctness currently exists for biological applications. Modern micro- array, digital PCR （dPCR）, and Next-Generation Sequencing （NGS） technologies frequently provide a means of coeff^cient of variation estimation for individual measurements. Using fold-change, and by making the assumption that measurements are normally distributed with known variances, we designed a novel statistical test that allows us to detect concomitantly, thus using the same formalism, differ- entially and similarly expressed genes （http：]]cds.ihes.fr）. Given two sets of gene measurements in different biological conditions, the probabilities of making type I and type II errors in stating that a gene is differentially or similarly expressed from one condition to the other can be calculated. Furthermore, a confidence interval for the fold-change can be delineated. Finally, we demonstrate that the assumption of normality can be relaxed to consider arbitrary distributions numerically. The Concomitant evaluation of Distinctness and Similarity （CDS） statistical test correctly estimates similarities and differences between measurements of gene expression. The imple- mentation, being time and memory efficient, allows the use of the CDS test in high-throughput data analysis such as microarray, dPCR, and NGS experiments. Importantly, the CDS test can be applied to the comparison of single measurements （N = 1） provided the var- iance （or coefficient of variation） of the signals is known, making CDS a valuable tool also in biomedical analysis where typically a single measurement per subject is available.

Finite-Size Conformational Transitions: A Unifying Concept Underlying Chromosome Dynamics

Investigating average thermodynamic quantities is not sufficient to understand conformational transitions of a finite-size polymer. We propose that such transitions are better described in terms of the probability distribution of some finite-size order parameter, and the evolution of this distribution as a control parameter varies. We demonstrate this claim for the coil-globule transition of a linear polymer and its mapping onto a two-state model. In a biological context, polymer models delineate the physical constraints experienced by the genome at different levels of organization,from DNA to chromatin to chromosome. We apply our finite-size approach to the formation of plectonemes in a DNA segment submitted to an applied torque and the ensuing helix-coil transition that can be numerically observed, with a coexistence of the helix and coil states in a range of parameters. Polymer models are also essential to analyze recent in vivo experiments providing the frequency of pairwise contacts between genomic loci. The probability distribution of these contacts yields quantitative information on the conformational fluctuations of chromosome regions. The changes observed in the shape of the distribution when the cell type or the physiological conditions vary may reveal an epigenetic modulation of the conformational constraints experienced by the chromosomes.

Effect of a Local Source or Sink of Inhibitor on Turing Patterns

We investigate a reaction-diffusion model in which a Turing pattern develops and reproduces the formation of periodic segments behind a propagating chemical wave front. The chemical scheme involves two species known as activator and inhibitor. The model can be used to mimic the formation of prevertebrae during the early development of vertebrate embryo. Deterministic and stochastic analyses of the reaction-diffusion processes are performed for two typical sets of parameter values, far from and close to the Turing bifurcation. The effects of a local source or sink of inhibitor on the growing structure are studied and successfully compared with experiments performed on chick embryos.We show that fluctuations may lead to the formation of additional prevertebra.

Coulomb Friction Driving Brownian Motors

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation(linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein–Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.

Scaling Properties of Field-Induced Superdiffusion in Continuous Time Random Walks

We consider a broad class of Continuous Time Random Walks(CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials,and a L′evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.

Periodic oscillation of quantum diffusion in coupled one-dimensional systems

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength.Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.